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Math Help - Inverse Trig Functions help

  1. #1
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    Inverse Trig Functions help

    I don't understand how you solve the following:

    1.) cos^-1(cos(-3pi/5). I supposed to find the exact value of the expression without using a calculator.

    2.) tan^-1(tan(5pi/7).

    3.) sin^-1(sin(4pi/5).

    Any help would be appreciated.
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  2. #2
    Junior Member astartleddeer's Avatar
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    Re: Inverse Trig Functions help

    Just think along the lines of, "One undoes the other."
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  3. #3
    MHF Contributor ebaines's Avatar
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    Re: Inverse Trig Functions help

    Quote Originally Posted by astartleddeer View Post
    Just think along the lines of, "One undoes the other."
    Not quite. Bear in mind that there are generally two answers to the inverse functions, but the range of the principal value is limited. For example sin(5pi/6) = 1/2, but arcsin(1/2) = pi/6 or 5pi/6, where pi/6 is the principal value. Hence arcsin(sin(5pi/6)) = pi/6 or 5 pi/6. For the arcsin and arctan functions the principal values are in the range -pi/2 to +pi/2, and for arccosine in the range of 0 to pi.
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